The Democratic Unionist leader and most recent first minister of Northern Ireland, Arlene Foster, says she wants to “bring stability to our nation” by backing Theresa May and the Conservatives to continue in power.

Foster said in Belfast on Friday afternoon that she was entering discussions with May over the details of any arrangement that would prop up a minority government.

Foster said the election in Northern Ireland, which saw 10 DUP MPs, including two new ones, elected to the Commons, was a “great result” for the union.

What is the DUP?

The Democratic Unionist party (DUP) is the largest political party in the devolved Northern Ireland assembly (where it shared power with the Irish republican party Sinn Féin until the start of this year) and with 10 MPs in the 2017 UK general election, its best-ever Westminster performance, the fifth-largest party in the House of Commons. Founded by Ian Paisley, it is led by Arlene Foster and its support of the Conservatives in parliament will allow Theresa May to form a government.

She confirmed that May had been in contact with her on Friday morning about gaining DUP support for a Tory administration.

“I make no apology for wanting the best for Northern Ireland and all of the union,” Foster said at the Stormont hotel in Belfast just across the road from the main entrance to the Stormont parliament, which remains shut down while talks begin next week to restore devolution.

The DUP leader said her party’s triumph and the result in Scotland, where the Scottish National party suffered losses, had “sent a clear and resounding message” to those who wished to tear the UK apart.

DUP figures insist their relationship with May’s team has been close since she became prime minister 11 months ago, and that late-night talks had been driven by their dismay at the possibility of Jeremy Corbyn becoming prime minister.

A DUP source said: “We want there to be a government. We have worked well with May. The alternative is intolerable. For as long as Corbyn leads Labour, we will ensure there’s a Tory PM.”

It has been reported that the two parties do not believe it necessary to enter a formal coalition to govern.

Senior DUP figures claimed they moved quickly to form an agreement to stop any chance of Corbyn entering No 10.

“The two parties [Labour and DUP] have worked well together for two years. There’s no reason to suppose they won’t continue to do so in future. But the point made time after time to Labour MPs remains: for as long as you allow yourselves to be led by an IRA cheerleader, you exclude yourselves from entering No 10,” said a DUP source.

The DUP’s “price” for propping up a new Tory government will include a promise that there will be no separate post-Brexit status for Northern Ireland, the party’s leader in Westminster has confirmed.

Nigel Dodds, re-elected as MP for Belfast North, said that among the DUP’s conditions would be an insistence that there be no deal that would keep the region with one foot still in the EU.

The DUP fears that separate status after Brexit – a key demand of Sinn Féin – would decouple Northern Ireland from the rest of the UK.

With one eye on the Brexit negotiations that begin in the next 10 days, Dodds said: “There are special circumstances in Northern Ireland and we will try to make sure these are recognised. As regards demands for special status within the European Union, no. Because that would create tariffs and barriers between Northern Ireland and our single biggest market, which is the rest of the United Kingdom.

“While we will focus on the special circumstances, geography and certain industries of Northern Ireland we will be pressing that home very strongly. Special status, however, within the European Union is a nonsense. Dublin doesn’t support it. Brussels doesn’t support it. The member states of the EU would never dream of it because it would open the door to a Pandora’s box of independence movements of all sorts. The only people who mentioned this are Sinn Féin.”

The DUP backed Brexit in last year’s EU referendum and regards as sacrosanct the UK’s decision to leave.

Sinn Féin has argued that because the Northern Ireland electorate voted by 56% to remain within Europe last year and that the region is the only one with a post-Brexit land border with the EU, the area should have special status.

When asked about what form of deal the DUP would consider, Dodds ruled out taking ministerial seats in a Conservative-led cabinet. Rather, the DUP is likely to back the Tories in confidence motions and support Conservative budgets.

“No, I am not thinking in those terms, I have to say,” Dodds said when asked about taking a cabinet seat, before joking that he would like to be secretary of state for Northern Ireland.

The DUP could also oppose Tory plans to cut winter fuel payments; Foster has pledged to “resist any assault” on what it sees as an important universal benefit in Northern Ireland.

The party, founded in 1971, maintains its socially conservative positions but has been transformed into an efficient political force by successive leaders since Ian Paisley stepped down in 2008.

While the Ulster Unionist party and the nationalist SDLP, both of which once dominated Northern Irish politics, lost all of their MPs, the DUP and Sinn Féin have flourished since the Anglo-Irish agreement.

Foster has developed close working relationships with ministers in the republic, though Sinn Féin has refused to return to the Stormont assembly while she is first minister.

Sinn Féin won seven seats in the election but Corbyn would not be able to rely on the support of those MPs as the party will continue its historical policy of boycotting Westminster.

Late on Thursday night, Gerry Adams, the Sinn Féin president, said his MPs would not be going to the House of Commons.

A senior Sinn Féin spokesman later told the Guardian there “wasn’t a snowball’s chance in hell” of the party ditching its abstentionism regarding Westminster.